原子基态函数对高次谐波谱影响的研究

强激光场和原子、分子相互作用产生高次谐波(High-order Harmonic Generation,HHG),高次谐波是重要的深紫外光的光源和探测原子分子动力学、原子分子结构等的有力工具.采用Lewenstein的理论,分别以s轨道和p轨道函数为基态函数,计算了惰性气体的高次谐波谱.计算发现,两种情况下得到的高次谐...     

非线性光学系统中的振幅立方压缩

本文研究了高次谐波产生及非谐振子模型两种非线性光学系统中存在光场振幅立方压缩的条件。     

一种新的非线性光学现象—Cascaded二级非线性光学效应

从Maxwell方程组出发,研究了一种新的非线性光学效应－Cascaded二级非线性现象,推导了依赖于光强的折射率变化－类克尔效应,分析了Cascaded非系性系数依赖于基波波长及波矢失配的变化规律,提出超晶格材料中产生Cascaded二级非线性效应的设想。     

一维模型原子高次谐波特性研究

通过数值计算求解含时的薛定谔方程,研究了在隧道电离区域16个激光脉冲作用于不同势阱势函数对应的一维模型原子产生的高次谐波特性,结果表明：在隧道电离区域势函数势阱的形状对一维模型原子的高次谐波强度产生较大影响,同时谐波的平台宽度的高阶区域也受到势函数的影响.     

一种非线性传输线梳状谱发生器的设计

以非线性传输线（NLTLs）理论和孤子波理论为基础,仿真设计了一种非线性传输线梳状谱发生器。该梳状谱发生器由5段具有不同布拉格截止频率的NLTL级联而成。测试结果显示,该梳状谱发生器的10次谐波输出功率为4.2dBm。本方法同传统方法相比,具有高次谐波输出功率大、电路结构简单、调试容易等优点。     

非线性Kronig-Penney超晶格中的波输运

通过二维实映射研究非线性Kronig-Penney(K-P)超晶格中的波输运,数值计算得到不同非线性系数的映射图以及相应的波位移平方在超晶格中的分布.非线性K-P超晶格中的非线性,对超晶格中波函数的Bloch波矢有明显的调节作用.随着非线性系数的增大,映射图由周期函数的有限个分立点变为准周期函数的一条闭合轨道、以及混沌吸引子.     

岩石超声谐波特征及其随应力的变化

岩石具有较强的非均质性和强衰减特性,谐波测量的难度较大。建立超声谐波测试实验系统,采用单频脉冲串(tone burst)激发、门控放大、脉冲反转和叠加等增强二次及高次谐波,研究岩石超声谐波的发育与振幅特征,定义名义非线性系数,分析单轴应力下岩石超声谐波及名义非线性系数随应力的变化。结果表明,超声谐波包含了丰富的岩石内部结构信息,表征了岩石的非线性特性,利用先进的仪器系统,采用谐波强化技术,可有效地获得岩石的超声谐波及其振幅,进行岩石非线性特性、微结构变化与损伤演化的监测。     

关于7阶Lax系KdV方程的非线性叠加公式

KdV方程最初由Korteweg和de Vries在研究非线性波理论时提出。本文用双线性算子方法研究了一个非线性方程,该方程是KdV方程向高阶的一个推广。利用Hirota的双线性算子公式,我们严格地证明了其Backlund变换的非线性叠加公式。     

水槽二维聚焦波浪特性试验研究

为更好地模拟波浪的非线性变化过程,给出了在实验室水槽中采用波浪聚焦产生极限波浪的方法.针对聚焦波浪的特点,采用波峰聚焦和波谷聚焦相加减的方法分析了其谐波分量的特性,结果表明,波浪之间的相互作用,导致低频和高频谐波分量的产生;非线性波浪随着输入波幅的增大而增大,高阶分量的频率范围随着输入频率范围的增大而增大.     

一维周期光学超晶格倍频特性分析

根据耦合波方程 ,导出了一维周期性光学超晶格中产生的倍频光的复振幅表达式。在准相位匹配条件下对不同参数进行了数值模拟 ,结果表明光学超晶格一个周期内正畴所占比例l/Λ和二次谐波的位相变化对二次谐波的转换效率具有较大影响。     

非线性叠加效应研究

对非线性叠加效应进行了研究,在Toda晶格中,当两孤立子运动方向相同时,其速度波的振幅的极大值是原来两波振幅之差,两波叠加的最大振幅是原来两波振幅之和。这些结果跟线性波叠加情况是完全不同的。     

Asymmetric energy flow in coupled nonlinear LC transmission line

We constructed a coupled LC transmission line and studied the propagation of waves in it. We found asymmetric energy flow when we changed the driving conditions at the boundary. We analyzed this change and believe that it occurs because of the bandpass characteristics of the LC transmission line and high-order harmonic waves induced by nonlinearities. The LC transmission line could be used to simulate a microscopic crystal lattice. Therefore, we hope to observe thermal rectification in the system. We investigated the dependence of the system on different parameters, and then discussed the multi-frequency condition to aid in experimental verification.     

非线性尘埃声波在含有2种不同温度离子的尘埃等离子体中的稳定性问题

在无磁场的尘埃等离子体中 ,由冷的尘埃颗粒和热的电子和离子组成的尘埃等离子体 ,对于有限的小振幅的非线性波的运动可以用KdV方程描述 .对由 2种不同温度离子的尘埃等离子体中的弱二维尘埃声波 ,得到了它所满足的KP方程 .并且发现 ,在横向扰动下 ,弱的非线性孤立波在尘埃等离子体中是稳定的 .在这个系统中既存在压缩孤立波又存在稀疏孤立波     

耦合非线性Schr-dinger方程组孤波解的格子Boltzmann模拟

使用格子Boltzmann方法模拟耦合非线性Schr-dinger方程组的孤波解. 构建了耦合非线性Schr-dinger方程组的格子Boltzmann模型, 并进行了数值实验. 数值实验结果表明, 格子Boltzmann方法是模拟耦合非线性Schrdinger方程组孤波解的有效方法.     

紧致型CIP方法数值模拟非线性波的传播

结合CIP方法和高阶紧致方法,提出了紧致型CIP方法,并利用该方法对非线性波进行数值模拟.该种方法采用小模板得到高精度的格式,通过3个算例可以看出其优越性.     

半地转近似下正压大气中的非线性波动

本文在半地转近似下讨论了正压模式大气中的非线性 Rossby 波.结果表明:这些非线性 Rossby 波可以是椭圆函数形式的波、孤立波或冲击波;产生这些波动的条件是由一个称之为“总能量”的物理量给出的,同时还敏感地依赖于相应量的初相值;文中还求出了一支没有线性近似对应的新频率的非线性波解,它纯粹是非线性效应的产物.     

利用格波与自旋波的对应关系研究晶体的物理性质

本文根据格波与自旋波的对应关系研究了晶体中的空格波,讨论了空格波对晶体物理性质的影响。     

Nonlinear dispersive scale Alfvén waves inmagnetosphere-ionosphere coupling: Physical processes and simulation results

Dispersive Alfvén waves(DAWs)have been demonstrated to play a significant role in auroral generation of the magnetosphereionosphere coupling system.Starting from a two fluid reduced MHD model,we summarize the frequency,temporal and spatial characteristics of magnetospheric DAWs.Then,the nonlinear kinetic and inertial scale Alfveén waves are studied,and we review some theoretical aspects and simulation results of dispersive Alfve′n waves in Earth’s magnetosphere.It is shown that dispersive standing Alfve′n waves can generate the field-aligned currents which transport energy into the auroral ionosphere,where it is dissipated by Joule heating and energy lost due to electron precipitation.The Joule dissipation can heat the ionospheric electron and produce changes in the ionospheric Pedersen conductivity.As a feedback,the conducting ionosphere can also strongly affect the magnetospheric currents. The ponderomotive force can cause the plasma to move along the field line,and generate ionospheric density cavity.The nonlinear structuring can lead to a dispersive scale to accelerate auroral particle,and the Alfvn waves can be trapped within the density cavity. Finally,we show the nonlinear decay of dispersive Alfvén waves related to two anti-propagating electron fluxes observed in the auroral zone.     

Observation of random-phase lattice solitons

The coherence of waves in periodic systems (lattices) is crucial to their dynamics, as interference effects, such as Bragg reflections, largely determine their propagation. Whereas linear systems allow superposition, nonlinearity introduces a non-trivial interplay between localization effects, coupling between lattice sites, and incoherence. Until recently, all research on solitary waves (solitons) in nonlinear lattices has involved only coherent waves. In such cases, linear dispersion or diffraction of wave packets can be balanced by nonlinear effects, resulting in coherent lattice (or 'discrete') solitons; these have been studied in many branches of science. However, in most natural systems, waves with only partial coherence are more common, because fluctuations (thermal, quantum or some other) can reduce the correlation length to a distance comparable to the lattice spacing. Such systems should support random-phase lattice solitons displaying distinct features. Here we report the experimental observation of random-phase lattice solitons, demonstrating their self-trapping and local periodicity in real space, in addition to their multi-peaked power spectrum in momentum space. We discuss the relevance of such solitons to other nonlinear periodic systems in which fluctuating waves propagate, such as atomic systems, plasmas and molecular chains.